1. Field of the Invention
The present invention relates to a two degree of freedom controller which performs an optimal control of process disturbances, and a control optimal for following target process values or setpoint values.
2. Description of the Related Art
PID controllers have been used in various fields of industry. Recently, digital PID controllers are used in increasing numbers, in place of analog PID controllers, and are now indispensable in controlling plants. A digital PID controller performs the following fundamental operation: EQU MV(s)=Kp{1+1/(T.sub.I s)+(T.sub.D s)}E(s) (1)
where MV(s) is a manipulative variable, E(s) is a deviation, Kp is a proportional gain, T.sub.I is an integral time, T.sub.D is a derivative time, s is a Laplace operator, .eta. is a coefficient, and 1/.eta. is a derivative gain. Equation (1) defines a PID control for a deviation E, which is generally known as "deviation PID control."
In the deviation PID control, however, the set point SV changes stepwise in many cases. In accordance with a change in the setpoint value SV, the PID controller performs an excessive D (Derivative) operation, whereby the manipulative variable MV greatly changes. As a result, the PID controller gives a shock to the controlled system. Alternatively the setpoint-following characteristic of the PID controller undergoes overshoot, whereby the controller inevitably performs a vibrational operation.
In recent years, a new type of a PID controller, which performs a D operation on PV, not on a deviation, has been put to practical use. This PID controller performs the following operation: EQU MV(s)=Kp[{1+1/(T.sub.I s)}E(s) -{(T.sub.D s)/(1+.eta.T.sub.D s)}PV(s)] (2)
where PV(s) is a control value supplied from the controlled system.
Equations (1) and (2) each define a one degree of freedom PID controlling operation. Only one set of PID parameters can be set. In actual controlled systems, the optimal PID parameter best for controlling the process disturbances and the PID parameter best for following the setpoint have different values.
In 1963, Issac I. Horowitz published an algorithm of two degrees of freedom PID (2DOF PID), in which two sets of parameters can be set independently and which enables a PID controller not only to control process disturbances efficiently, but also to follow the setpoint values accurately. This algorithm has since been applied to many PID controllers, which are actually used, carrying out high-level plant control. In this 2DOF PID algorithm, PID parameters optimal for controlling process disturbances are set first. When the setpoint value is altered, the PID parameters are automatically changed in accordance with the coefficient of the setpoint filter selected for the new setpoint value.
FIG. 1 is a block diagram showing a 2DOF PID controller of the type used commonly, which comprises a setpoint filter means H(s) and a PID controller (derivative-on-PV type). As is shown in FIG. 1, the setpoint filter means H(s) is connected to the input of the PID controller, and comprises a lead/lag means 1, a 1st lag means 2, an incomplete derivative means 3, a subtracter means 4, an incomplete integral means 5, an adder means 6. The lead/lag means 1 imparts a lead or a lag to a setpoint value SV. The 1st lag means 2 imparts a 1st lag to the setpoint value SV. The incomplete derivative means 3 sets an upper limit to the derivative gain, and also delay derivative operation. The subtracter means 4 subtracts the output of the 1st lag means 2 from the output of the incomplete derivative means 3. The incomplete integral means 5 delays the output of the subtracter means 4. The adder means 6 adds the output of the lead/lag means 1 and that of the incomplete derivative means 5. The output SV.sub.0 of the adder means 6, or the output SV.sub.0 of the setpoint filter means H(s) is supplies to the PID controller as a setpoint.
The PID controller of the derivative-on-PV type comprises a deviation-calculating means 7, a non-linear means 8, a PI-control operation means 9, a subtracter means 10, and an incomplete derivative means 11. The deviation-calculating means 7 receives the output SV.sub.0 of the adder means 6 and also the control value PV supplied from a controlled system 12, and calculates a deviation E from the output SV.sub.0 and the control value PV. The deviation E, thus obtained, is input to the non-linear means 8. The non-linear means 8 performs non-linear operations on the deviation E, which include dead-band operation, deviation-square operation, and gain-change operation, thus producing an output. The output of the means 8 is input to the PI-control operation means 9. The operation means 9 performs a PI-control operation on the output of the non-linear means 8, said PI-control operation defined by the first term of the right side of equation (2), whereby producing a PI-control value. The PI-control value is supplied to the subtracter means 10.
Meanwhile the control value PV is supplied from the controlled system 12 to the incomplete derivative means 11. The incomplete derivative means 11 performs an incomplete derivative operation on the control value PV, said incomplete derivative operation defined by the second term of the right side of equation (2), whereby producing an incomplete derivative value. The incomplete derivative value is input to the subtracter means 10. The subtracter means 10 subtracts the incomplete derivative value from the PI-control value, thereby obtaining a manipulative variable MV.
The manipulative variable MV is supplied to an adder means 13, to which a process-disturbance signal D is also supplied. The adder means 13 adds the variable MV and the signal D. The sum of the variable MV and the signal D is input to the controlled system 12, whereby the system 12 is controlled such that the control value PV becomes equal to the setpoint value SV.sub.0, that is, SV.sub.0 =PV.
Hence, the algorithm C.sub.D (s) for controlling process disturbances is represented by the following: EQU C.sub.D (s)=Kp{1+1/(T.sub.I s)+(T.sub.D s)/(1+.eta.T.sub.D s)}(3)
On the other hand, the algorithm C.sub.SV (s) for controlling the setpoint value is defined as follows: EQU C.sub.SV (s)=Kp[.alpha.+{1/(T.sub.I s)-.beta..sub.0 /(1+T.sub.I .multidot.s)}+(.gamma..sub.0 T.sub.D s)/(1+.eta.T.sub.D s)] (4)
First, parameters Kp, T.sub.I, and T.sub.D are set to such values that the 2DOF PID controller may have an optimal process-disturbance control characteristic. Then, 2DOF coefficients .alpha., .beta..sub.0, and .gamma..sub.0 are determined so that the 2DOF PID controller may have the best possible setpoint-following characteristic. Once the 2DOF PID controller has an optimal process-disturbance control characteristic and an optimal setpoint-following characteristic, the parameters Kp, T.sub.I, and T.sub.D can be varied in accordance with the coefficients .alpha., .beta..sub.0, and .gamma..sub.0 thus coping with changes in the control value PV. As a result of this, the controller can perform a two degree of freedom PID control.
The two degree of freedom PID control, described above, is advantageous in many respects, but disadvantageous in the following respects.
1. As is evident from equation (4), the 2DOF coefficients .alpha., .beta..sub.0 and .gamma..sub.0 are independent of one another, though they must be interrelated. Hence, the coefficients .beta..sub.0 and .gamma..sub.0 must be changed independently when the coefficient .alpha. is changed. It takes much time to adjust the coefficients .beta..sub.0 and .gamma..sub.0.
2. As has been described, the setpoint filter means H(s) and the PID controller (derivative-on-PV type) have 1st lag means and incomplete derivative means, and several tens to several thousands of 2DOF PID controls are effected in most cases in order to control a plant. Hence, a plant-controlling system needs to have a number of 1st lag means and a number of incomplete derivative means. The load of the system is great, making it difficult for the system to operate at high speed and inevitably not rendering the system a low-capacity one.
3. To control a plant, a deviation is subjected to non-linear operation in many cases. The non-linear operation cannot be achieved with ease, accuracy or freedom.
That is, a non-linear operation is performed on a deviation in many cases to control a plant, since the plant cannot be controlled in accordance with the deviation E only, because of the characteristic of the controlled system 12. This is why the non-linear means is connected to the input of the PI-control operation means 9, for performing non-linear operations on the deviation E, such as dead-band operation, deviation-square operation, gain-change operation, and gap operation. Since the incomplete derivative means 11 is bypassed to the output of the PI-control operation mean 9, the output of the incomplete derivative means 11 is not subjected to the non-linear operation. Consequently, the results of the non-linear operation are not accurate, inevitably reducing the reliability of the two degree of freedom PID control.